Physics! #24 University Physics 4.2

You’ve probably heard Newton’s First somewhere as “a body in motion tends to stay in motion, and a body at rest tends to stay at rest.” That layman’s statement is actually pretty solid. And, you can see how it could be made more general simply by combining it to say “When it comes to motion, an object tends to keep doing what it’s doing.”

The book’s more rigorous form goes “A body acted on by no net force moves with constant velocity (which my be zero) and zero acceleration.”

Here’s how I like to think of it: Say you’re somewhere in deep space, far from strong effects of gravity, and you’re floating in some direction. You’ll continue going in that direction forever. Why? Because why would you stop going on that direction? That is, if you are to change direction or speed (or both), SOMETHING has to happen to cause that change.

If you were staying still, a similar rule would apply. You won’t start moving until something happens to cause you to move. That something is net force.

Interestingly, since the issue is NET force on you, the following scenario is possible: You’re sitting motionless in space. Then, you see rocks hurtling toward you from either side. You say “yes! Now’s my chance to start moving!” Then, by dumb luck, each rock hits you from the opposite direction at the same time, resulting in two equal smacks against you. So, the rocks ricochet off, and you gain no speed.

The flip side to this, though, is that even a tiny amount of force will cause you to move. So, say you’re drinking a soda in space. You belch, then press a button on your space suit to eject that belch into space. As a result, you’ll be propelled away from the belch! You’re a motionless object in space, so anything done by you (as a self-contained system) has to result in zero net force. So, when you send a belch one way, your body goes the other way. If it didn’t, there’s be more than zero net force on the system called you.

Offhand, the human body has at least half a dozen such propulsion mechanisms if you ever get trapped in zero G. Interestingly, rockets work along pretty much this exact principle. But, more on that later…

The fact that stuff in the universe tends to not change its momentum is called Inertia. In casual language, we often refer to social things as having inertia. Like, a political campaign that can’t get anywhere is said to be up against inertia. Or, a political campaign that’s really doing so well that might be hard to stop even if there are impediments to it is said to benefit from inertia. So, you see, the casual use of the word is actually pretty descriptive.

I like to think of inertia as the universe saying “fuck off.” Objects in reality do whatever they were gonna do anyway unless you go and change something about that. Otherwise, fuck off.

The mathematical version of the fuck off principle goes like this:

For an object at constant velocity (aka equilibrium)

Note that there’s an F on the left, and on O on the right. This is short for fuck off.

Inertial Frames of Reference

The more dorkly-inclined among you may have some mental objections to the above. You might say “HEY! FUCK! WHAT ABOUT DIFFERENT REFERENCE FRAMES?”

So, let me make up a weird example that’ll elucidate and then clarify the problem.

Imagine you are a car gnome. Car gnomes are microscopic and only live for 5 seconds, but they move very quickly, so they experience a lot in that time. Car gnomes also live in cars, hence the name.

Imagine you happen to be born as Car goes around a sharp turn. Imagine also that you are the Isaac Newton of car gnomes, and you attempt to decipher the laws of Car. You end up with a law that’s similar to the ones human have, only there’s a modifier. Why? Because Car is accelerating by moving around a circle, everything in your universe always pulls in the cardinal direction car gnomes call “passenger side.” So, you can’t just say “Sum of forces at equilibrium = 0.” Why? Because in Car, you can set an object on the floor, let it go, and it will always go toward the passenger’s side accelerating at v^2/R. You decide to call this Passenger Force.

Passenger Force is odd to you because all the other forces you observe when you look outside Car are more consistent. For example, you’ve discovered Force of Gravity, which affects things in Car, but also affects other Cars, and even affects the movement of stars and planets. Passenger Force seems to have no analog outside of Car. Plus, according to the ancient library of Cargnomia, before you were born, Passenger Force was lower. And, many generations ago, it didn’t even exist!

In physics terms, Passenger Force is a “fictitious force.” It’s not like gravity or EM, which are the same everywhere. It’s a modifier to your force equation based on local conditions.

NOW, imagine you’re an ancient car gnome from 100 generations earlier, when Car was just sitting in the garage. You wouldn’t ever have come up with Passenger Force. You would only have known about the same forces that humans know about. And, your equations would be the same as ours too.

So, what’s the difference between the modern car gnome’s reference frame and the ancient car gnome’s reference frame? The modern car gnome is in a reference frame that is NOT at equilibrium. Car is experiencing acceleration. So, we say it’s in a “non-inertial reference frame.”

The ancient car gnome’s reference frame is a small area on the surface of Earth. Although it actually does experience acceleration (since the earth is spinning, after all), it’s verrrrry small. Remember, centripetal acceleration is v^2/R, and on a body the size of Earth, that R is enormous. In fact, at the equator, that acceleration is only about 3/1000ths of little g.

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This may lead you to say “what use is Newton’s First if it doesn’t work in non-inertial reference frames.” Well, you’ll probably spend most of your life at various points on the surface of the Earth. Wherever you are on this planet, you’re basically on an inertial reference frame.

In fact, Newton’s First is a good way to judge whether you’re in an inertial reference frame. If our Isaac Newton car gnome from earlier knew the laws of physics, he could have deduced that he was in a rotating body. In other words, as the book says “A frame of reference in which Newton’s first law is valid is called an inertial frame of reference.”